On Elastic Wave Band Gap And Vibro-acoustic Attenuation Of Lightweight Honeycomb Structure Based On Phononic Crystal

Light-weight sandwich structures have the advantages of being lightweight,having a specific strength,high specific stiffness.Therefore,they have been widely used in the field of engineering.However,from the perspective of the law of mass,these properties of high specific stiffness and strength lead to a poor vibro-acoustic performance.Therefore,the question of how to solve this contradiction between good mechanical properties and high vibro-acoustic performance is a key concern for many scientists.In this study,the theory of phononic crystal band gaps is utilized to improve the vibroacoustic performance of honeycomb sandwich structures.To this end,a systematic analysis,including theoretical,numerical and experimental methods,is conducted to explore the design method of high-efficiency vibro-acoustic control of lightweight structures.Various studies have shown that the low-frequency vibro-acoustic attenuation can be realized for lightweight structures utilizing phononic crystal metamaterials.However,most of the researchers mainly focus on the regulation of elastic wave,and there are few studies,in which both,lightweight high-strength and low-frequency vibro-acoustic properties are considered simultaneously.To solve the above problems,a new phononic crystal honeycomb sandwich structure is designed based on the local resonance mechanism.To localize the low-frequency bandgaps,an analytical model based on Hamilton’s principle and the energy averaging technique is developed and is confirmed by a three-dimensional numerical simulation.Moreover,the effective mass density is determined analytically to give a physical insight into the wave control mechanism.Then,the dynamic behavior of the proposed honeycomb sandwich structure is investigated analytically.A finite element simulation and experimental measurements are performed to demonstrate the validity and accuracy of this dynamic model.Results show that the proposed honeycomb sandwich structure exhibits an excellent vibration suppression performance,as well as a significant tunability.Furthermore,to claim multifunctionality,the out-of-plane compression behavior is analyzed experimentally.Experimental results indicate that mechanical properties of the proposed honeycomb sandwich structure are significantly improved in comparison with a traditional honeycomb sandwich structure.The proposed strategy is a novel multi-functional combination,which can help realize vibration suppression and high mechanical efficiency.In addition,considering the wide application of cylindrical structures in the engineering field,this design method is extended to cylindrical honeycomb sandwich structures.Firstly,an analytical model based on Love shell theory is established to investigate the dispersion relations of an orthotropic cylindrical shell with local resonators.The low-frequency band gaps and the presence of negative effective mass density are confirmed analytically.Subsequently,the influences of curvature and orthotropy on wave propagation behavior are discussed and the prediction formula for band gaps is defined for engineering design.Then,a new cylindrical honeycomb sandwich structure is designed and fabricated by introducing local resonators into a square honeycomb sandwich structure.The forced vibration response of the proposed cylindrical honeycomb sandwich structure is studied using both numerical simulations and experimental validation.Furthermore,a cylindrical structure with a stiffened plate inside is studied numerically and experimentally,which confirms its vibration suppression performance in actual applications.As is established,sound isolation is one of the important methods to realize vibration and noise reduction.For the honeycomb sandwich structure with large unit cells,there is a low-frequency sound isolation valley related to the local resonance of face sheets.To eliminate this sound isolation valley,the vibro-acoustic model of the locally resonant honeycomb sandwich structure is constructed based on the spatial harmonic expansion method.The influence of resonator position on the sound transmission behavior is systematically studied.The results show that the resonator distributed on the side wall of the honeycomb core has no contribution to the elimination of this sound isolation valley.The resonator distributed at the center of the face sheet can effectively improve the sound transmission performance of the honeycomb sandwich structure.Then,by studying the effects of damping and graded resonators,the optimal design method is determined to weaken the side effects of resonators.Moreover,the sound transmission under excitation of oblique incidence sound waves is also investigated.Compared with the method of filling porous materials,the proposed design method can better eliminate the sound isolation valley,and,more importantly,the mass of the resonator is only 1.23% of that of the porous materials.In order to further broaden the band gap width,a multilayer honeycomb sandwich structure with broadband coupled band gap is designed by combining the local resonance effect and the Bragg scattering mechanism.A transfer matrix model based on the effective mass is developed to comprehend the mechanism of band gap formation.Furthermore,a strategy for designing a broadband low-frequency coupled band gap is established analytically.Then,a four-layer honeycomb sandwich meta-structure is designed and fabricated based on the proposed design strategy.Experimental results demonstrate the successful realization of a broadband coupled band gap with the introduction of the resonators with meticulously selected parameters.Finally,the designed honeycomb sandwich structure is applied to a vibration isolator.The experimental results show that the proposed multi-layer honeycomb sandwich structure has a higher vibration isolation performance compared with that of the conventional rubber material.